Question

Consider the hypotheses shown below. Given that x overbarequals57​, sigmaequals13​, nequals35​, alphaequals0.10​, complete parts a and b. Upper H 0​: muless than or equals54 Upper H 1​: mugreater than54

Answer 1

GIVEN:

Sample size

Sample mean

Population standard deviation

HYPOTHESIS:

The hypothesis is given by,

(That is, the true population mean is less than or equal to 54.)

(That is, the true population mean is greater than 54.)

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows standard normal distribution.

CALCULATION:

  

  

CRITICAL VALUE:

The right tailed (since ) z critical value at significance level is .

DECISION RULE:

CONCLUSION:

Since the calculated z test statistic (1.37) is greater than the z critical value (1.28), we reject the null hypothesis and conclude that the true population mean is greater than 54.

P VALUE:

The right tailed p value for the test statistic is,

{Since }

Using the z table, the probability value is the value with corresponding row 1.3 and column 0.07.

DECISION RULE:

CONCLUSION:

Since the calculated p value (0.0853) is less than the significance level , we reject the null hypothesis and conclude that the true population mean is greater than 54.